Random effects model

About: Random effects model is a research topic. Over the lifetime, 8388 publications have been published within this topic receiving 438823 citations. The topic is also known as: random effects & random effect.

Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation

Abstract: Popular frameworks for studying habitat selection include resource-selection functions (RSFs) and step-selection functions (SSFs), estimated using logistic and conditional logistic regression, respectively. Both frameworks compare environmental covariates associated with locations animals visit with environmental covariates at a set of locations assumed available to the animals. Conceptually, slopes that vary by individual, that is, random coefficient models, could be used to accommodate inter-individual heterogeneity with either approach. While fitting such models for RSFs is possible with standard software for generalized linear mixed-effects models (GLMMs), straightforward and efficient one-step procedures for fitting SSFs with random coefficients are currently lacking. To close this gap, we take advantage of the fact that the conditional logistic regression model (i.e. the SSF) is likelihood-equivalent to a Poisson model with stratum-specific fixed intercepts. By interpreting the intercepts as a random effect with a large (fixed) variance, inference for random-slope models becomes feasible with standard Bayesian techniques, or with frequentist methods that allow one to fix the variance of a random effect. We compare this approach to other commonly applied alternatives, including models without random slopes and mixed conditional regression models fit using a two-step algorithm. Using data from mountain goats (Oreamnos americanus) and Eurasian otters (Lutra lutra), we illustrate that our models lead to valid and feasible inference. In addition, we conduct a simulation study to compare different estimation approaches for SSFs and to demonstrate the importance of including individual-specific slopes when estimating individual- and population-level habitat-selection parameters. By providing coded examples using integrated nested Laplace approximations (INLA) and Template Model Builder (TMB) for Bayesian and frequentist analysis via the R packages R-INLA and glmmTMB, we hope to make efficient estimation of RSFs and SSFs with random effects accessible to anyone in the field. SSFs with individual-specific coefficients are particularly attractive since they can provide insights into movement and habitat-selection processes at fine-spatial and temporal scales, but these models had previously been very challenging to fit.

Restricted spatial regression in practice: Geostatistical models, confounding, and robustness under model misspecification

Abstract: In spatial generalized linear mixed models (SGLMMs), covariates that are spatially smooth are often collinear with spatially smooth random effects. This phenomenon is known as spatial confounding and has been studied primarily in the case where the spatial support of the process being studied is discrete (e.g., areal spatial data). In this case, the most common approach suggested is restricted spatial regression (RSR) in which the spatial random effects are constrained to be orthogonal to the fixed effects. We consider spatial confounding and RSR in the geostatistical (continuous spatial support) setting. We show that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. We propose a posterior predictive approach to alleviating this potential problem and discuss the appropriateness of RSR in a variety of situations. We illustrate RSR and SGLMM approaches through simulation studies and an analysis of malaria frequencies in The Gambia, Africa. Copyright © 2015 John Wiley & Sons, Ltd.

Small area estimation: the EBLUP estimator based on spatially correlated random area effects

Abstract: This paper deals with small area indirect estimators under area level random effect models when only area level data are available and the random effects are correlated. The performance of the Spatial Empirical Best Linear Unbiased Predictor (SEBLUP) is explored with a Monte Carlo simulation study on lattice data and it is applied to the results of the sample survey on Life Conditions in Tuscany (Italy). The mean squared error (MSE) problem is discussed illustrating the MSE estimator in comparison with the MSE of the empirical sampling distribution of SEBLUP estimator. A clear tendency in our empirical findings is that the introduction of spatially correlated random area effects reduce both the variance and the bias of the EBLUP estimator. Despite some residual bias, the coverage rate of our confidence intervals comes close to a nominal 95%.

Fixed Effects, Random Effects, and Hybrid Models for Causal Analysis

Abstract: Longitudinal data are becoming increasingly common in social science research. In this chapter, we discuss methods for exploiting the features of longitudinal data to study causal effects. The methods we discuss are broadly termed fixed effects and random effects models. We begin by discussing some of the advantages of fixed effects models over traditional regression approaches and then present a basic notation for the fixed effects model. This notation serves also as a baseline for introducing the random effects model, a common alternative to the fixed effects approach. After comparing fixed effects and random effects models – paying particular attention to their underlying assumptions – we describe hybrid models that combine attractive features of each. To provide a deeper understanding of these models, and to help researchers determine the most appropriate approach to use when analyzing longitudinal data, we provide three empirical examples. We also briefly discuss several extensions of fixed/random effects models. We conclude by suggesting additional literature that readers may find helpful.